Except for his last sentence where he used the word "evolved," Charles Darwin never mentioned "evolution" in The Origin of Species. Instead, he used the phrase "descent with modification." Evolutionary classification today is based on those two central features of evolution: groups of organisms descend from a common ancestor and, with the passage of time, acquire modifications.

Cladistic analysis, also known as cladistics and phylogenetic systematics, is the main approach of classification used in contemporary evolutionary biology. The German taxonomist Willi Hennig developed cladistics in 1950, but his work was not widely known until it was translated into English in 1966. After scientists began using molecular data in classification, Hennig's cladistics became increasingly adopted. Cladistic analysis starts with the assumption that evolution is a branching process: ancestral species split into descendant species, and these relationships can be represented much like family trees represent genealogies. The "trees" obtained by such analyses are called phylogenies. These phylogenies should be viewed as testable hypotheses, subject to either confirmation or rejection depending on new evidence. Of course, hypotheses differ as to how much support they have. Some are so well supported (such as that humans share a closer common ancestor to chimpanzees than either share with lemurs) that they are exceedingly unlikely to be overturned.

In cladistic analysis, groups of organisms, known as taxa, are arranged into clades that are then nested into larger clades. The term "taxa" (singular "taxon") can be applied to groups of any size. Taxa that are each others' closest relatives are called sister taxa. Each clade should be monophyletic; that is, all members share a single common ancestor, and all descendants of that ancestor are included in the clade. In contrast, a polyphyletic group is one in which the members are derived from more than one common ancestor. What if all of a particular clade's members share a common ancestor but not all taxa that share that common ancestor are included in that group? Such a group is called paraphyletic.

Taxonomists following cladistic analysis place taxa into clades based on the derived character states that the taxa share. For example, a wing is a character. The presence or absence of a wing would be alternative character states. Other features of a wing (such as its shape and size, and how it develops) could also be character states. Aside from the presumption that characters are independent of one another, any trait can be a character. In principle, there is no difference between the analysis of morphological and molecular characters. The characters used most often in molecular phylogenies are the nucleotide positions of the examined DNA molecule(s); thus, the character states are the actual nucleotides at that position. Shared, derived characteristics are known as synapomorphies.

That taxonomists would classify taxa based on similarity makes sense. After all, like goes with like. But why would they consider only the derived shared character states? Why not consider all character states, including those that are primitive? The rationale is that the primitive characters do not reveal information about which groups share more recent common ancestors; the primitive character states would only contribute noise to the system. In classifying different groups of birds that all fly, whether they fly does not contribute information. In fact, in classifying flightless birds, considering the ancestral state (flighted) can actually distort the obtained phylogeny away from the true phylogeny. For these reasons, only synapomorphies (shared, derived character states) are considered in the analysis. In practice, taxonomists often have difficulty in distinguishing between which character states are primitive and which are derived.

For what reasons can taxa share synapomorphies? One possibility is that they share a common ancestor. This is called homology. While cladistic analysis assumes that most synapomorphies will arise by homology, they can arise by other ways. One possibility is convergence: different lineages that do not share a recent common ancestor evolve to the same character state. An obvious example is that both bats and birds have wings; however, these were independently derived, most likely owing to similar selective forces. This example is obvious because so many other characters place bats closer to non-winged clades (other mammals) than to birds. Yet, less obvious cases can be resolved only after cladistic analysis. Another possible reason why non-homologous character states can be similar is a reversal in which mutation or selection causes the derived character state to revert to the ancestral state.

How does cladistic analysis work, especially given the possibility of conflicting data generated by reversals and convergence? Taxonomists, like scientists in general, start with the principle of parsimony - that the shortest, most simple, and direct path is most likely to be the correct one. In one commonly used method, parsimony analysis, the taxonomist searches for the most parsimonious tree; that is, the one that requires the fewest number of evolutionary transitions. Consider the example in Figure 3: three possible phylogenies exist. Based on the data given, for phylogeny (A) to occur, we must postulate a total of x evolutionary changes. Phylogeny (B) requires postulating y changes and phylogeny (C) requires postulating z changes. Because (B) requires the fewest changes, it is the most parsimonious tree.

The most parsimonious tree may not necessarily represent the true phylogenetic relationships. Perhaps certain types of transitions are more likely or evolved more easily than are others. It is often difficult to know before doing the analysis, which changes are most likely. Thus, taxonomists generally resort to the fallback position that all changes are equally likely. There are some cases, particularly with molecular data, where there is good prior knowledge of variation in the likelihoods of different changes. For instance, certain types of mutations are more likely than others are. Transitions (changes from a purine - A or G - to the other purine, or a pyrimidine - C or T - to the other pyrimidine) are more likely than transversions (changes from a purine to a pyrimidine or vice-versa). Using increasingly statistical techniques, such as maximum likelihood analysis, taxonomists can adjust for these situations.

Figure 4 shows an example of an unrooted tree. Unrooted trees do not display the directionality of evolution, only patterns of relatedness. A unrooted tree can be rooted, but for any given unrooted tree there are many possible rooted trees that can be derived. Rooting a tree usually requires identification and use of an outgroup - a taxon that is more distantly related than the taxa contained within the tree. For instance, given an unrooted tree containing the great apes (humans, chimpanzees, gorillas, orangutans, and gibbons), one could use a species of monkeys, such as baboons, as an outgroup. (See the Human Evolution unit.) In practice, taxonomists often use multiple outgroups to refine the analyses.